The aim of this Research Unit is to present the state-of-the-art of control theory in what concerns systems governed by differential equations and systems. We consider optimal control and controllability questions both from the theoretical and numerical viewpoints.
In all cases, we assume that a system modeling the phenomenon under study (the state equation) is given. Some data in this system (the control variables) can be chosen more or less freely. In optimal control problems, the aim is to minimize a cost that depends on the solution of the model system (the state) and also on the control variables. In controllability theory, the aim is to choose the control in order to get the state we wish after a finite working time interval.
Usually, the main questions are: (a) Do “good” and “optimal” controls exist? (b) If yes, which is the cost (the effort) we have to pay to get these? (c) How can we compute them? We will try to provide answers (or partial answers) to these questions for many systems of different kinds. In most cases, open questions appear. Some of them have been selected as research projects for the students.
Schedule of the Course 2: